“Remove the rune batteries via transmat to open the prison doors.”
Head forward in the Asylum. There are 2 towers in this massive room. One on the left and one on the right. Each has a Hive battery that you are going to need to disable to move forward.
When it is time to deactivate the runes, work with your fireteam and only go after one at a time. Once the first rune is deactivated, then deactivate the second.
To get to the left one, head to the edge of the main platform and make the jump over to the moving platforms. Check your timing and wait for one of them to be coming toward you. While you will see a Shrieker, it is presently inactivate and will not activate until you start interacting with the battery. You do need to worry about some Wizards that are guarding the batteries. Be wary of them as you approach.
Once you are on the platform with the Hive battery you need simply scan it with Ghost. Still, take out the Wizards guarding it first to remove them as a threat to yourself. After that, scan the Hive battery. Once you do, immediately start shooting the Shrieker that has been sitting there. Stay on the platform, deal with the Shrieker and wait for the chest to open. Once it does, interact with it again to remove the battery and deactivate the rune.
Head back to the main platform. Clear out the Hive on it. After that, reload because the Taken are coming.